$A$ radioactive sample $S_1$ having an activity $5 \mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10 \mu Ci$. The half-lives of $S_1$ and $S_2$ can be

$A$ certain radioactive substance has a half-life of $5\, years$. Thus, for a nucleus in a sample of the element, the probability of decay in $10\, years$ is ......... $\%$

$A$ nuclear power plant supplying electrical power to a village uses a radioactive material of half-life $T$ years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is $12.5 \%$ of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of $n T$ years,then the value of $n$ is

Radioactive nuclei $A$ and $B$ disintegrate into $C$ with half-lives $T$ and $2T$. At $t = 0$,the number of nuclei of each $A$ and $B$ is $x$. The number of nuclei of $C$ when the rate of disintegration of $A$ and $B$ are equal is:

$A$ parent nucleus $X$ decays into a daughter nucleus $Y$,which in turn decays into $Z$. The half-lives of $X$ and $Y$ are $40000 \, yr$ and $20 \, yr$,respectively. In a certain sample,it is found that the number of $Y$ nuclei hardly changes with time. If the number of $X$ nuclei in the sample is $4 \times 10^{20}$,the number of $Y$ nuclei present in it is

$A$ radioactive element has a half-life of $15$ years. What is the fraction that will decay in $30$ years?